FYS-STK4155/doc/LectureNotes/_build/jupyter_execute/week46.ipynb

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    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
    "doconce format html week46.do.txt --no_mako -->\n",
    "<!-- dom:TITLE: Week 46: Decision Trees, Ensemble methods  and Random Forests -->"
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    "# Week 46: Decision Trees, Ensemble methods  and Random Forests\n",
    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
    "\n",
    "Date: **Week 46, November 13-17**"
   ]
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    "## Plan for week 46\n",
    "\n",
    "**Active learning sessions on Tuesday and Wednesday.**\n",
    "\n",
    "  * Work and Discussion of project 2\n",
    "\n",
    "  * Discussion of project 3 as well\n",
    "\n",
    "  \n",
    "\n",
    "**Material for the lecture on Thursday November 16, 2023.**\n",
    "\n",
    "  * Thursday: Basics of decision trees, classification and regression algorithms and ensemble models \n",
    "\n",
    "  * Readings and Videos:\n",
    "\n",
    "    * These lecture notes\n",
    "\n",
    "    * [Video of lecture](https://youtu.be/PMswUwhYa7k)\n",
    "\n",
    "    * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesNov16.pdf)    \n",
    "\n",
    "    * [Video on Decision trees](https://www.youtube.com/watch?v=RmajweUFKvM&ab_channel=Simplilearn)\n",
    "\n",
    "    * Decision Trees: Geron's chapter 6 covers decision trees while ensemble models, voting and bagging are discussed in chapter 7. See also lecture from [STK-IN4300, lecture 7](https://www.uio.no/studier/emner/matnat/math/STK-IN4300/h20/slides/lecture_7.pdf). Chapter 9.2 of Hastie et al contains also a good discussion."
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    "## Decision trees, overarching aims\n",
    "\n",
    "We start here with the most basic algorithm, the so-called decision\n",
    "tree. With this basic algorithm we can in turn build more complex\n",
    "networks, spanning from homogeneous and heterogenous forests (bagging,\n",
    "random forests and more) to one of the most popular supervised\n",
    "algorithms nowadays, the extreme gradient boosting, or just\n",
    "XGBoost. But let us start with the simplest possible ingredient.\n",
    "\n",
    "Decision trees are supervised learning algorithms used for both,\n",
    "classification and regression tasks.\n",
    "\n",
    "The main idea of decision trees\n",
    "is to find those descriptive features which contain the most\n",
    "**information** regarding the target feature and then split the dataset\n",
    "along the values of these features such that the target feature values\n",
    "for the resulting underlying datasets are as pure as possible.\n",
    "\n",
    "The descriptive features which reproduce best the target/output features are normally  said\n",
    "to be the most informative ones. The process of finding the **most\n",
    "informative** feature is done until we accomplish a stopping criteria\n",
    "where we then finally end up in so called **leaf nodes**."
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    "## Basics of a tree\n",
    "\n",
    "A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
    "and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
    "\n",
    "The leaf nodes\n",
    "contain the predictions we will make for new query instances presented\n",
    "to our trained model. This is possible since the model has \n",
    "learned the underlying structure of the training data and hence can,\n",
    "given some assumptions, make predictions about the target feature value\n",
    "(class) of unseen query instances."
   ]
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    "## A typical Decision Tree with its pertinent Jargon, Classification Problem\n",
    "\n",
    "<!-- dom:FIGURE: [DataFiles/cancer.png, width=600 frac=0.8] -->\n",
    "<!-- begin figure -->\n",
    "\n",
    "<img src=\"DataFiles/cancer.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
    "<!-- end figure -->\n",
    "\n",
    "This tree was produced using the Wisconsin cancer data (discussed here as well, see code examples below) using **Scikit-Learn**'s decision tree classifier. Here we have used the so-called **gini** index (see below) to split the various branches."
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    "## General Features\n",
    "\n",
    "The overarching approach to decision trees is a top-down approach.\n",
    "\n",
    "* A leaf provides the classification of a given instance.\n",
    "\n",
    "* A node specifies a test of some attribute of the instance.\n",
    "\n",
    "* A branch corresponds to a possible values of an attribute.\n",
    "\n",
    "* An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute in the given example.\n",
    "\n",
    "This process is then repeated for the subtree rooted at the new\n",
    "node."
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    "## How do we set it up?\n",
    "\n",
    "In simplified terms, the process of training a decision tree and\n",
    "predicting the target features of query instances is as follows:\n",
    "\n",
    "1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
    "\n",
    "2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process\n",
    "\n",
    "3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the *predictions* we want to make for new query instances\n",
    "\n",
    "4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
    "\n",
    "Then we are essentially done!"
   ]
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   "source": [
    "## Decision trees and Regression"
   ]
  },
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     "text": [
      "2nd degree coefficients:\n",
      "zero power:  -2.877168286047408\n",
      "first power:  -0.052836183775253814\n",
      "second power:  -1.4881344092288954e-05\n"
     ]
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_9_1.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_9_2.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "steps=250\n",
    "\n",
    "distance=0\n",
    "x=0\n",
    "distance_list=[]\n",
    "steps_list=[]\n",
    "while x<steps:\n",
    "    distance+=np.random.randint(-1,2)\n",
    "    distance_list.append(distance)\n",
    "    x+=1\n",
    "    steps_list.append(x)\n",
    "plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
    "\n",
    "steps_list=np.asarray(steps_list)\n",
    "distance_list=np.asarray(distance_list)\n",
    "\n",
    "X=steps_list[:,np.newaxis]\n",
    "\n",
    "#Polynomial fits\n",
    "\n",
    "#Degree 2\n",
    "poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly=poly_features.fit_transform(X)\n",
    "\n",
    "lin_reg=LinearRegression()\n",
    "poly_fit=lin_reg.fit(X_poly,distance_list)\n",
    "b=lin_reg.coef_\n",
    "c=lin_reg.intercept_\n",
    "print (\"2nd degree coefficients:\")\n",
    "print (\"zero power: \",c)\n",
    "print (\"first power: \", b[0])\n",
    "print (\"second power: \",b[1])\n",
    "\n",
    "z = np.arange(0, steps, .01)\n",
    "z_mod=b[1]*z**2+b[0]*z+c\n",
    "\n",
    "fit_mod=b[1]*X**2+b[0]*X+c\n",
    "plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
    "plt.title(\"Polynomial Regression\")\n",
    "\n",
    "plt.xlabel(\"Steps\")\n",
    "plt.ylabel(\"Distance\")\n",
    "\n",
    "#Degree 10\n",
    "poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
    "X_poly10=poly_features10.fit_transform(X)\n",
    "\n",
    "poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
    "\n",
    "y_plot=poly_fit10.predict(X_poly10)\n",
    "plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#Decision Tree Regression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "regr_1=DecisionTreeRegressor(max_depth=2)\n",
    "regr_2=DecisionTreeRegressor(max_depth=5)\n",
    "regr_3=DecisionTreeRegressor(max_depth=7)\n",
    "regr_1.fit(X, distance_list)\n",
    "regr_2.fit(X, distance_list)\n",
    "regr_3.fit(X, distance_list)\n",
    "\n",
    "X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
    "y_1 = regr_1.predict(X_test)\n",
    "y_2 = regr_2.predict(X_test)\n",
    "y_3=regr_3.predict(X_test)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure()\n",
    "plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
    "plt.plot(X_test, y_1, color=\"red\",\n",
    "         label=\"max_depth=2\", linewidth=2)\n",
    "plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
    "plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
    "\n",
    "plt.xlabel(\"Data\")\n",
    "plt.ylabel(\"Darget\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9defc5e7",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Building a tree, regression\n",
    "\n",
    "There are mainly two steps\n",
    "1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$.  \n",
    "\n",
    "2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
    "\n",
    "How do we construct the regions $R_1,\\dots,R_J$?  In theory, the\n",
    "regions could have any shape. However, we choose to divide the\n",
    "predictor space into high-dimensional rectangles, or boxes, for\n",
    "simplicity and for ease of interpretation of the resulting predictive\n",
    "model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
    "MSE, given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97bfeb0f",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60e3b6f5",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $\\overline{y}_{R_j}$  is the mean response for the training observations \n",
    "within box $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a950a77",
   "metadata": {
    "editable": true
   },
   "source": [
    "## A top-down approach, recursive binary splitting\n",
    "\n",
    "Unfortunately, it is computationally infeasible to consider every\n",
    "possible partition of the feature space into $J$ boxes.  The common\n",
    "strategy is to take a top-down approach\n",
    "\n",
    "The approach is top-down because it begins at the top of the tree (all\n",
    "observations belong to a single region) and then successively splits\n",
    "the predictor space; each split is indicated via two new branches\n",
    "further down on the tree. It is greedy because at each step of the\n",
    "tree-building process, the best split is made at that particular step,\n",
    "rather than looking ahead and picking a split that will lead to a\n",
    "better tree in some future step."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7aa91ac",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Making a tree\n",
    "\n",
    "In order to implement the recursive binary splitting we start by selecting\n",
    "the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecfe94f2",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j < s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4970af3",
   "metadata": {
    "editable": true
   },
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85bd3a40",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j \\geq s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ea5b535",
   "metadata": {
    "editable": true
   },
   "source": [
    "so that we obtain the lowest MSE, that is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5672b44",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "999be0b7",
   "metadata": {
    "editable": true
   },
   "source": [
    "which we want to minimize by considering all predictors\n",
    "$x_1,x_2,\\dots,x_p$.  We consider also all possible values of $s$ for\n",
    "each predictor. These values could be determined by randomly assigned\n",
    "numbers or by starting at the midpoint and then proceed till we find\n",
    "an optimal value.\n",
    "\n",
    "For any $j$ and $s$, we define the pair of half-planes where\n",
    "$\\overline{y}_{R_1}$ is the mean response for the training\n",
    "observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
    "response for the training observations in $R_2(j,s)$.\n",
    "\n",
    "Finding the values of $j$ and $s$ that minimize the above equation can be\n",
    "done quite quickly, especially when the number of features $p$ is not\n",
    "too large.\n",
    "\n",
    "Next, we repeat the process, looking\n",
    "for the best predictor and best cutpoint in order to split the data\n",
    "further so as to minimize the MSE within each of the resulting\n",
    "regions. However, this time, instead of splitting the entire predictor\n",
    "space, we split one of the two previously identified regions. We now\n",
    "have three regions. Again, we look to split one of these three regions\n",
    "further, so as to minimize the MSE. The process continues until a\n",
    "stopping criterion is reached; for instance, we may continue until no\n",
    "region contains more than five observations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac6a5d56",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Pruning the tree\n",
    "\n",
    "The above procedure is rather straightforward, but leads often to\n",
    "overfitting and unnecessarily large and complicated trees. The basic\n",
    "idea is to grow a large tree $T_0$ and then prune it back in order to\n",
    "obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
    "lead to smaller variance and better interpretation at the cost of a\n",
    "little more bias.\n",
    "\n",
    "The so-called Cost complexity pruning algorithm gives us a\n",
    "way to do just this. Rather than considering every possible subtree,\n",
    "we consider a sequence of trees indexed by a nonnegative tuning\n",
    "parameter $\\alpha$.\n",
    "\n",
    "Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63deb833",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Cost complexity pruning\n",
    "\n",
    "For each value of $\\alpha$  there corresponds a subtree $T \\in T_0$ such that"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f4c860f",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd542b6e",
   "metadata": {
    "editable": true
   },
   "source": [
    "is as small as possible. Here $\\overline{T}$ is \n",
    "the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
    "rectangle (i.e. the subset of predictor space)  corresponding to the $m$-th terminal node.\n",
    "\n",
    "The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
    "complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
    "subtree $T$ will simply equal $T_0$, \n",
    "because then the above equation just measures the\n",
    "training error. \n",
    "However, as $\\alpha$ increases, there is a price to pay for\n",
    "having a tree with many terminal nodes. The above equation will\n",
    "tend to be minimized for a smaller subtree. \n",
    "\n",
    "It turns out that as we increase $\\alpha$ from zero\n",
    "branches get pruned from the tree in a nested and predictable fashion,\n",
    "so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
    "easy. We can select a value of $\\alpha$ using a validation set or using\n",
    "cross-validation. We then return to the full data set and obtain the\n",
    "subtree corresponding to $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5099f78",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Schematic Regression Procedure\n",
    "\n",
    "**Building a Regression Tree.**\n",
    "\n",
    "1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
    "\n",
    "2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
    "\n",
    "3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
    "\n",
    "  * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
    "\n",
    "  * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
    "\n",
    "  * Finally  we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
    "\n",
    "4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88e2ce13",
   "metadata": {
    "editable": true
   },
   "source": [
    "## A Classification Tree\n",
    "\n",
    "A classification tree is very similar to a regression tree, except\n",
    "that it is used to predict a qualitative response rather than a\n",
    "quantitative one. Recall that for a regression tree, the predicted\n",
    "response for an observation is given by the mean response of the\n",
    "training observations that belong to the same terminal node. In\n",
    "contrast, for a classification tree, we predict that each observation\n",
    "belongs to the most commonly occurring class of training observations\n",
    "in the region to which it belongs. In interpreting the results of a\n",
    "classification tree, we are often interested not only in the class\n",
    "prediction corresponding to a particular terminal node region, but\n",
    "also in the class proportions among the training observations that\n",
    "fall into that region."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fab855d",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Growing a classification tree\n",
    "\n",
    "The task of growing a\n",
    "classification tree is quite similar to the task of growing a\n",
    "regression tree. Just as in the regression setting, we use recursive\n",
    "binary splitting to grow a classification tree. However, in the\n",
    "classification setting, the MSE cannot be used as a criterion for making\n",
    "the binary splits.  A natural alternative to MSE is the **classification\n",
    "error rate**. Since we plan to assign an observation in a given region\n",
    "to the most commonly occurring error rate class of training\n",
    "observations in that region, the classification error rate is simply\n",
    "the fraction of the training observations in that region that do not\n",
    "belong to the most common class. \n",
    "\n",
    "When building a classification tree, either the Gini index or the\n",
    "entropy are typically used to evaluate the quality of a particular\n",
    "split, since these two approaches are more sensitive to node purity\n",
    "than is the classification error rate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dc57784",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Classification tree, how to split nodes\n",
    "\n",
    "If our targets are the outcome of a classification process that takes\n",
    "for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
    "is to set up the splitting criteria for each node.\n",
    "\n",
    "We define a PDF $p_{mk}$ that represents the number of observations of\n",
    "a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
    "this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
    "observations of this class in the region $R_m$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a23d427",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78e66687",
   "metadata": {
    "editable": true
   },
   "source": [
    "We let $p_{mk}$ represent the majority class of observations in region\n",
    "$m$. The three most common ways of splitting a node are given by\n",
    "\n",
    "* Misclassification error"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9157055f",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "259d56c7",
   "metadata": {
    "editable": true
   },
   "source": [
    "* Gini index $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66f8ee1a",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7478d6d0",
   "metadata": {
    "editable": true
   },
   "source": [
    "* Information entropy or just entropy $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30737ebf",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c145a6a4",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Visualizing the Tree, Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c04064d0",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
      "0          17.99         10.38          122.80     1001.0          0.11840   \n",
      "1          20.57         17.77          132.90     1326.0          0.08474   \n",
      "2          19.69         21.25          130.00     1203.0          0.10960   \n",
      "3          11.42         20.38           77.58      386.1          0.14250   \n",
      "4          20.29         14.34          135.10     1297.0          0.10030   \n",
      "..           ...           ...             ...        ...              ...   \n",
      "564        21.56         22.39          142.00     1479.0          0.11100   \n",
      "565        20.13         28.25          131.20     1261.0          0.09780   \n",
      "566        16.60         28.08          108.30      858.1          0.08455   \n",
      "567        20.60         29.33          140.10     1265.0          0.11780   \n",
      "568         7.76         24.54           47.92      181.0          0.05263   \n",
      "\n",
      "     mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
      "0             0.27760         0.30010              0.14710         0.2419   \n",
      "1             0.07864         0.08690              0.07017         0.1812   \n",
      "2             0.15990         0.19740              0.12790         0.2069   \n",
      "3             0.28390         0.24140              0.10520         0.2597   \n",
      "4             0.13280         0.19800              0.10430         0.1809   \n",
      "..                ...             ...                  ...            ...   \n",
      "564           0.11590         0.24390              0.13890         0.1726   \n",
      "565           0.10340         0.14400              0.09791         0.1752   \n",
      "566           0.10230         0.09251              0.05302         0.1590   \n",
      "567           0.27700         0.35140              0.15200         0.2397   \n",
      "568           0.04362         0.00000              0.00000         0.1587   \n",
      "\n",
      "     mean fractal dimension  ...  worst radius  worst texture  \\\n",
      "0                   0.07871  ...        25.380          17.33   \n",
      "1                   0.05667  ...        24.990          23.41   \n",
      "2                   0.05999  ...        23.570          25.53   \n",
      "3                   0.09744  ...        14.910          26.50   \n",
      "4                   0.05883  ...        22.540          16.67   \n",
      "..                      ...  ...           ...            ...   \n",
      "564                 0.05623  ...        25.450          26.40   \n",
      "565                 0.05533  ...        23.690          38.25   \n",
      "566                 0.05648  ...        18.980          34.12   \n",
      "567                 0.07016  ...        25.740          39.42   \n",
      "568                 0.05884  ...         9.456          30.37   \n",
      "\n",
      "     worst perimeter  worst area  worst smoothness  worst compactness  \\\n",
      "0             184.60      2019.0           0.16220            0.66560   \n",
      "1             158.80      1956.0           0.12380            0.18660   \n",
      "2             152.50      1709.0           0.14440            0.42450   \n",
      "3              98.87       567.7           0.20980            0.86630   \n",
      "4             152.20      1575.0           0.13740            0.20500   \n",
      "..               ...         ...               ...                ...   \n",
      "564           166.10      2027.0           0.14100            0.21130   \n",
      "565           155.00      1731.0           0.11660            0.19220   \n",
      "566           126.70      1124.0           0.11390            0.30940   \n",
      "567           184.60      1821.0           0.16500            0.86810   \n",
      "568            59.16       268.6           0.08996            0.06444   \n",
      "\n",
      "     worst concavity  worst concave points  worst symmetry  \\\n",
      "0             0.7119                0.2654          0.4601   \n",
      "1             0.2416                0.1860          0.2750   \n",
      "2             0.4504                0.2430          0.3613   \n",
      "3             0.6869                0.2575          0.6638   \n",
      "4             0.4000                0.1625          0.2364   \n",
      "..               ...                   ...             ...   \n",
      "564           0.4107                0.2216          0.2060   \n",
      "565           0.3215                0.1628          0.2572   \n",
      "566           0.3403                0.1418          0.2218   \n",
      "567           0.9387                0.2650          0.4087   \n",
      "568           0.0000                0.0000          0.2871   \n",
      "\n",
      "     worst fractal dimension  \n",
      "0                    0.11890  \n",
      "1                    0.08902  \n",
      "2                    0.08758  \n",
      "3                    0.17300  \n",
      "4                    0.07678  \n",
      "..                       ...  \n",
      "564                  0.07115  \n",
      "565                  0.06637  \n",
      "566                  0.07820  \n",
      "567                  0.12400  \n",
      "568                  0.07039  \n",
      "\n",
      "[569 rows x 30 columns]\n",
      "     malignant  benign\n",
      "0            1       0\n",
      "1            1       0\n",
      "2            1       0\n",
      "3            1       0\n",
      "4            1       0\n",
      "..         ...     ...\n",
      "564          1       0\n",
      "565          1       0\n",
      "566          1       0\n",
      "567          1       0\n",
      "568          0       1\n",
      "\n",
      "[569 rows x 2 columns]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "cancer = load_breast_cancer()\n",
    "X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
    "print(X)\n",
    "y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
    "y = pd.get_dummies(y)\n",
    "print(y)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/cancer.dot\",\n",
    "    feature_names=cancer.feature_names,\n",
    "    class_names=cancer.target_names,\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da6433b2",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Visualizing the Tree, The Moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7a884220",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import os\n",
    "\n",
    "np.random.seed(42)\n",
    "X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/moons.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dfa7512",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Other ways of visualizing the trees\n",
    "\n",
    "**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bc172ee1",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0.9166666666666666, 'X[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
       " Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
       " Text(0.5769230769230769, 0.75, 'X[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
       " Text(0.3076923076923077, 0.5833333333333334, 'X[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
       " Text(0.15384615384615385, 0.4166666666666667, 'X[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
       " Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
       " Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.46153846153846156, 0.4166666666666667, 'X[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
       " Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
       " Text(0.5384615384615384, 0.25, 'X[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
       " Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
       " Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.8461538461538461, 0.5833333333333334, 'X[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
       " Text(0.7692307692307693, 0.4166666666666667, 'X[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
       " Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
       " Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
       " Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_41_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn import tree\n",
    "X, y = load_iris(return_X_y=True)\n",
    "tree_clf = tree.DecisionTreeClassifier()\n",
    "tree_clf = tree_clf.fit(X, y)\n",
    "# and then plot the tree\n",
    "tree.plot_tree(tree_clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7996538",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Printing out as text\n",
    "\n",
    "Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
    "This method doesn’t require the installation of external libraries and is more compact:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "18c69627",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|--- petal width (cm) <= 0.80\n",
      "|   |--- class: 0\n",
      "|--- petal width (cm) >  0.80\n",
      "|   |--- petal width (cm) <= 1.75\n",
      "|   |   |--- class: 1\n",
      "|   |--- petal width (cm) >  1.75\n",
      "|   |   |--- class: 2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.tree import export_text\n",
    "iris = load_iris()\n",
    "decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
    "decision_tree = decision_tree.fit(iris.data, iris.target)\n",
    "r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d734081",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Algorithms for Setting up Decision Trees\n",
    "\n",
    "Two algorithms stand out in the set up of decision trees:\n",
    "1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
    "\n",
    "2. The ID3 algorithm based on the computation of the information gain for classification\n",
    "\n",
    "We discuss both algorithms with applications here. The popular library\n",
    "**Scikit-Learn** uses the CART algorithm. For classification problems\n",
    "you can use either the **gini** index or the **entropy** to split a tree\n",
    "in two branches."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17e0e2f9",
   "metadata": {
    "editable": true
   },
   "source": [
    "## The CART algorithm for Classification\n",
    "\n",
    "For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
    "This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
    "\n",
    "How do we find these two quantities?\n",
    "We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
    "The cost function it tries to minimize is then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73fc933b",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ca9923",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset  and $m_{\\mathrm{left/right}}$\n",
    " is the number of instances in the left/right subset\n",
    "\n",
    "Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
    "and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
    "$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
    "hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
    "$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feb6fee3",
   "metadata": {
    "editable": true
   },
   "source": [
    "## The CART algorithm for Regression\n",
    "\n",
    "The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
    "training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24b0aea3",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a01610a",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here the MSE for a specific node is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c28e4ab",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76dc3641",
   "metadata": {
    "editable": true
   },
   "source": [
    "with"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60f57c10",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c3e3601",
   "metadata": {
    "editable": true
   },
   "source": [
    "the mean value of all observations in a specific node.\n",
    "\n",
    "Without any regularization, the regression task for decision trees, \n",
    "just like for classification tasks, is  prone to overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0be42f06",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Why binary splits?\n",
    "\n",
    "It is custom to split to a tree uising binary splits. The reason is\n",
    "that multiway splits fragment the data too quickly, leaving\n",
    "insufficient data at the next level down.  Multiway splits can be\n",
    "achieved by a series of binary split and this is normally preferred."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42ed666b",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Computing a Tree using the Gini Index\n",
    "\n",
    "Consider the following example with attributes/features and two\n",
    "possible outcomes (classes)  for each attribute.  Assume we wish to find some\n",
    "correlations between the average grade of a student as function of the\n",
    "number of hours studied and hours slept. We want also to correlate the\n",
    "grade in a given course with the general trend, whether the students\n",
    "recently has gotten grades below average or above.\n",
    "\n",
    "We have three features/attributes\n",
    "1. Trend of average grades before present course, classified as either below  or above  the average grade of the whole class  \n",
    "\n",
    "2. The number of hours studies, classified again as either higher (more than 3 hours per day) or lower . Here we have used a standard for one $ECTS$ which is scaled to 25-30 hours of work for a semester which lasts 18 weeks, with 15 weeks of lectures and 3 weeks for exams, assuming a total of 30 ECTS per semester. \n",
    "\n",
    "3. The number of hours slept as high for more than $8$ hours and below  for less than 8 hours of sleep, classified again as either high or low\n",
    "\n",
    "4. The final grade whether it is above or below average"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ab2f2b9",
   "metadata": {
    "editable": true
   },
   "source": [
    "## The Table\n",
    "\n",
    "<table class=\"dotable\" border=\"1\">\n",
    "<thead>\n",
    "<tr><th align=\"center\">Grade Trend</th> <th align=\"center\">Hours slept</th> <th align=\"center\">Hours Studied</th> <th align=\"center\">Grade</th> </tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   High           </td> <td align=\"center\">   Low              </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   High           </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   Low              </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   High           </td> <td align=\"center\">   High             </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   Low              </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   High           </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "</tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df7b209e",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Computing the various Gini Indices\n",
    "\n",
    "In computations we will translate all classes into numbers. Being\n",
    "these binary classes, they can easily be split into ones and zeros.\n",
    "\n",
    "**Gini index for Average trend.**\n",
    "\n",
    "[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f77f79d",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Computing the various Gini Indices, Hours slept\n",
    "\n",
    "**Gini index for hour slept.**\n",
    "\n",
    "[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "737f4e14",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Computing the various Gini Indices, Hours studied\n",
    "\n",
    "**Gini index for hour studied.**\n",
    "\n",
    "[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)\n",
    "\n",
    "For final tree, see the above handwritten notes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2c139d1",
   "metadata": {
    "editable": true
   },
   "source": [
    "## A possible code using Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d0089709",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Grade Trend</th>\n",
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      "text/plain": [
       "   Grade Trend  Hours slept  Hours Studied  Grade\n",
       "0            1            0              1      1\n",
       "1            0            1              0      0\n",
       "2            1            0              1      1\n",
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       "5            1            0              0      0\n",
       "6            0            1              1      0\n",
       "7            0            0              1      0\n",
       "8            1            0              0      0\n",
       "9            1            1              1      1"
      ]
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 1]\n",
      " [0 1 0]\n",
      " [1 0 1]\n",
      " [1 1 1]\n",
      " [0 0 1]\n",
      " [1 0 0]\n",
      " [0 1 1]\n",
      " [0 0 1]\n",
      " [1 0 0]\n",
      " [1 1 1]]\n",
      "Train set accuracy with Decision Tree: 1.00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "infile = open(data_path(\"grades.csv\"),'r')\n",
    "\n",
    "# Read the experimental data with Pandas\n",
    "from IPython.display import display\n",
    "grades = pd.read_csv(infile)\n",
    "grades = pd.DataFrame(grades)\n",
    "display(grades)\n",
    "# Features and targets\n",
    "X = grades.loc[:, grades.columns != 'Grade'].values\n",
    "y = grades.loc[:, grades.columns == 'Grade'].values\n",
    "print(X)\n",
    "# Then do a Classification tree\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X, y)\n",
    "print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
    "#transfer to a decision tree graph\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/grade.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/grade.dot -o DataFiles/grades.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f185aef",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Further example: Computing the Gini index\n",
    "\n",
    "The next example we will look at is a classical one in many Machine\n",
    "Learning applications. Based on various meteorological features, we\n",
    "have several so-called attributes which decide whether we at the end\n",
    "will do some outdoor activity like skiing, going for a bike ride etc\n",
    "etc.  The table here contains the feautures **outlook**, **temperature**,\n",
    "**humidity** and **wind**.  The target or output is whether we ride\n",
    "(True=1) or whether we do something else that day (False=0). The\n",
    "attributes for each feature are then sunny, overcast and rain for the\n",
    "outlook, hot, cold and mild for temperature, high and normal for\n",
    "humidity and weak and strong for wind.\n",
    "\n",
    "The table here summarizes the various attributes and\n",
    "<table class=\"dotable\" border=\"1\">\n",
    "<thead>\n",
    "<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr><td align=\"center\">   1      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   2      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   3      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   4      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   5      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   6      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   7      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   8      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   9      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   10     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   11     </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   12     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   13     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   14     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "</tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe73a991",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Simple Python Code to read in Data and perform Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9b082c47",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  (0, 0)\t1.0\n",
      "  (0, 7)\t1.0\n",
      "  (0, 9)\t1.0\n",
      "  (0, 13)\t1.0\n",
      "  (1, 3)\t1.0\n",
      "  (1, 5)\t1.0\n",
      "  (1, 8)\t1.0\n",
      "  (1, 12)\t1.0\n",
      "  (2, 3)\t1.0\n",
      "  (2, 5)\t1.0\n",
      "  (2, 8)\t1.0\n",
      "  (2, 11)\t1.0\n",
      "  (3, 1)\t1.0\n",
      "  (3, 5)\t1.0\n",
      "  (3, 8)\t1.0\n",
      "  (3, 12)\t1.0\n",
      "  (4, 2)\t1.0\n",
      "  (4, 6)\t1.0\n",
      "  (4, 8)\t1.0\n",
      "  (4, 12)\t1.0\n",
      "  (5, 2)\t1.0\n",
      "  (5, 4)\t1.0\n",
      "  (5, 10)\t1.0\n",
      "  (5, 12)\t1.0\n",
      "  (6, 2)\t1.0\n",
      "  :\t:\n",
      "  (8, 12)\t1.0\n",
      "  (9, 3)\t1.0\n",
      "  (9, 4)\t1.0\n",
      "  (9, 10)\t1.0\n",
      "  (9, 12)\t1.0\n",
      "  (10, 2)\t1.0\n",
      "  (10, 6)\t1.0\n",
      "  (10, 10)\t1.0\n",
      "  (10, 12)\t1.0\n",
      "  (11, 3)\t1.0\n",
      "  (11, 6)\t1.0\n",
      "  (11, 10)\t1.0\n",
      "  (11, 11)\t1.0\n",
      "  (12, 1)\t1.0\n",
      "  (12, 6)\t1.0\n",
      "  (12, 8)\t1.0\n",
      "  (12, 11)\t1.0\n",
      "  (13, 1)\t1.0\n",
      "  (13, 5)\t1.0\n",
      "  (13, 10)\t1.0\n",
      "  (13, 12)\t1.0\n",
      "  (14, 2)\t1.0\n",
      "  (14, 6)\t1.0\n",
      "  (14, 8)\t1.0\n",
      "  (14, 11)\t1.0\n",
      "Train set accuracy with Decision Tree: 0.73\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "infile = open(data_path(\"rideclass.csv\"),'r')\n",
    "\n",
    "# Read the experimental data with Pandas\n",
    "from IPython.display import display\n",
    "ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
    "ridedata = pd.DataFrame(ridedata)\n",
    "\n",
    "# Features and targets\n",
    "X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
    "y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
    "\n",
    "# Create the encoder.\n",
    "encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
    "# Assume for simplicity all features are categorical.\n",
    "encoder.fit(X)    \n",
    "# Apply the encoder.\n",
    "X = encoder.transform(X)\n",
    "print(X)\n",
    "# Then do a Classification tree\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X, y)\n",
    "print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
    "#transfer to a decision tree graph\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/ride.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df9287bb",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Computing the Gini Factor\n",
    "\n",
    "The above functions (gini, entropy and misclassification error) are\n",
    "important components of the so-called CART algorithm. We will discuss\n",
    "this algorithm below after we have discussed the information gain\n",
    "algorithm ID3.\n",
    "\n",
    "In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "00d95a16",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "Split: [X3 < 1.000]\n"
     ]
    }
   ],
   "source": [
    "# Split a dataset based on an attribute and an attribute value\n",
    "def test_split(index, value, dataset):\n",
    "\tleft, right = list(), list()\n",
    "\tfor row in dataset:\n",
    "\t\tif row[index] < value:\n",
    "\t\t\tleft.append(row)\n",
    "\t\telse:\n",
    "\t\t\tright.append(row)\n",
    "\treturn left, right\n",
    " \n",
    "# Calculate the Gini index for a split dataset\n",
    "def gini_index(groups, classes):\n",
    "\t# count all samples at split point\n",
    "\tn_instances = float(sum([len(group) for group in groups]))\n",
    "\t# sum weighted Gini index for each group\n",
    "\tgini = 0.0\n",
    "\tfor group in groups:\n",
    "\t\tsize = float(len(group))\n",
    "\t\t# avoid divide by zero\n",
    "\t\tif size == 0:\n",
    "\t\t\tcontinue\n",
    "\t\tscore = 0.0\n",
    "\t\t# score the group based on the score for each class\n",
    "\t\tfor class_val in classes:\n",
    "\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
    "\t\t\tscore += p * p\n",
    "\t\t# weight the group score by its relative size\n",
    "\t\tgini += (1.0 - score) * (size / n_instances)\n",
    "\treturn gini\n",
    "\n",
    "# Select the best split point for a dataset\n",
    "def get_split(dataset):\n",
    "\tclass_values = list(set(row[-1] for row in dataset))\n",
    "\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
    "\tfor index in range(len(dataset[0])-1):\n",
    "\t\tfor row in dataset:\n",
    "\t\t\tgroups = test_split(index, row[index], dataset)\n",
    "\t\t\tgini = gini_index(groups, class_values)\n",
    "\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
    "\t\t\tif gini < b_score:\n",
    "\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
    "\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
    " \n",
    "dataset = [[0,0,0,0,0],\n",
    "            [0,0,0,1,1],\n",
    "            [1,0,0,0,1],\n",
    "            [2,1,0,0,1],\n",
    "            [2,2,1,0,1],\n",
    "            [2,2,1,1,0],\n",
    "            [1,2,1,1,1],\n",
    "            [0,1,0,0,0],\n",
    "            [0,2,1,0,1],\n",
    "            [2,1,1,0,1],\n",
    "            [0,1,1,1,1],\n",
    "            [1,1,0,1,1],\n",
    "            [1,0,1,0,1],\n",
    "            [2,1,0,1,0]]\n",
    "\n",
    "split = get_split(dataset)\n",
    "print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6452b51",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Regression trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3a98b310",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Quadratic training set + noise\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m, 1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.randn(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1f8e183f",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2, random_state=42)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c91981e",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Final regressor code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c9b69f54",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_72_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "53db8f73",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_73_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
    "y_pred1 = tree_reg1.predict(x1)\n",
    "y_pred2 = tree_reg2.predict(x1)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"No restrictions\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3be38ddf",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Pros and cons of trees, pros\n",
    "\n",
    "* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
    "\n",
    "* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
    "\n",
    "* No feature normalization needed\n",
    "\n",
    "* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
    "\n",
    "* Can model nonlinear relationships\n",
    "\n",
    "* Can model interactions between the different descriptive features\n",
    "\n",
    "* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4aaab5f",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Disadvantages\n",
    "\n",
    "* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
    "\n",
    "* If continuous features are used the tree may become quite large and hence less interpretable\n",
    "\n",
    "* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
    "\n",
    "* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
    "\n",
    "* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
    "\n",
    "* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
    "\n",
    "* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
    "\n",
    "However, by aggregating many decision trees, using methods like\n",
    "bagging, random forests, and boosting, the predictive performance of\n",
    "trees can be substantially improved."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0010cb58",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods\n",
    "\n",
    "As stated above and seen in many of the examples discussed here about\n",
    "a single decision tree, we often end up overfitting our training\n",
    "data. This normally means that we have a high variance. Can we reduce\n",
    "the variance of a statistical learning method?\n",
    "\n",
    "This leads us to a set of different methods that can combine different\n",
    "machine learning algorithms or just use one of them to construct\n",
    "forests and jungles of trees, homogeneous ones or heterogenous\n",
    "ones. These methods are recognized by different names which we will\n",
    "try to explain here. These are\n",
    "\n",
    "1. Voting classifiers\n",
    "\n",
    "2. Bagging and Pasting\n",
    "\n",
    "3. Random forests\n",
    "\n",
    "4. Boosting methods, from adaptive to Extreme Gradient Boosting (XGBoost)\n",
    "\n",
    "We discuss these methods here."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3a71c11",
   "metadata": {
    "editable": true
   },
   "source": [
    "## An Overview of Ensemble Methods\n",
    "\n",
    "<!-- dom:FIGURE: [DataFiles/ensembleoverview.png, width=600 frac=0.8] -->\n",
    "<!-- begin figure -->\n",
    "\n",
    "<img src=\"DataFiles/ensembleoverview.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aef5e772",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Why Voting?\n",
    "\n",
    "The idea behind boosting, and voting as well can be phrased as follows:\n",
    "**Can a group of people somehow arrive at highly\n",
    "reasoned decisions, despite the weak judgement of the individual\n",
    "members?**\n",
    "\n",
    "The aim is to create a good classifier by combining several weak classifiers.\n",
    "**A weak classifier is a classifier which is able to produce results that are only slightly better than guessing at random.**\n",
    "\n",
    "The basic approach is to apply repeatedly (in boosting this is done in an iterative way) a weak classifier to modifications of the data.\n",
    "In voting we simply apply the law of large numbers while in boosting we give more weight to misclassified data in\n",
    "each iteration.  \n",
    "\n",
    "Decision trees play an important role as our weak classifier. They serve as the basic method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a30b02f8",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Tossing coins\n",
    "\n",
    "The simplest case is a so-called voting ensemble. To illustrate this,\n",
    "think of yourself tossing coins with a biased outcome of 51 per cent\n",
    "for heads and 49% for tails. With only few tosses,\n",
    "you may not clearly see this distribution for heads and tails. However, after some\n",
    "thousands of tosses, there will be a clear majority of heads.  With 2000 tosses\n",
    "you should see approximately 1020 heads and 980 tails.\n",
    "\n",
    "We can then state that the outcome is a clear majority of heads. If\n",
    "you do this ten thousand times, it is easy to see that there is a 97%\n",
    "likelihood of a majority of heads.\n",
    "\n",
    "Another example would be to collect all polls before an\n",
    "election. Different polls may show different likelihoods for a\n",
    "candidate winning with say a majority  of the popular vote. The majority vote\n",
    "would then consist in many polls indicating that this candidate will\n",
    "actually win.\n",
    "\n",
    "The example here shows how we can implement the coin tossing case,\n",
    "clealry demostrating that after some tosses we see the [law of large](https://en.wikipedia.org/wiki/Law_of_large_numbers)\n",
    "numbers kicking in."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3afd02ed",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Standard imports first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4a1b7a89",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Common imports\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c32e96d",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Simple Voting Example, head or tail"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4d1c99f7",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x350 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_83_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "heads_proba = 0.51\n",
    "coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)\n",
    "cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)\n",
    "plt.figure(figsize=(8,3.5))\n",
    "plt.plot(cumulative_heads_ratio)\n",
    "plt.plot([0, 10000], [0.51, 0.51], \"k--\", linewidth=2, label=\"51%\")\n",
    "plt.plot([0, 10000], [0.5, 0.5], \"k-\", label=\"50%\")\n",
    "plt.xlabel(\"Number of coin tosses\")\n",
    "plt.ylabel(\"Heads ratio\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.axis([0, 10000, 0.42, 0.58])\n",
    "save_fig(\"votingsimple\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0e3f1dc",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Using the Voting Classifier\n",
    "\n",
    "We can use the voting classifier on other data sets, here the exciting binary case of two distinct objects using the make moons functionality of **Scikit-Learn**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c3d00f7d",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.872\n",
      "SVC 0.888\n",
      "VotingClassifier 0.896\n",
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.872\n",
      "SVC 0.888\n",
      "VotingClassifier 0.912\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.ensemble import VotingClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "log_clf = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
    "rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n",
    "svm_clf = SVC(gamma=\"auto\", random_state=42)\n",
    "\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='hard')\n",
    "\n",
    "voting_clf.fit(X_train, y_train)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))\n",
    "\n",
    "log_clf = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
    "rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n",
    "svm_clf = SVC(gamma=\"auto\", probability=True, random_state=42)\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='soft')\n",
    "voting_clf.fit(X_train, y_train)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0d12f2c",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Voting and Bagging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1bbde2a9",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "VotingClassifier(estimators=[('lr', LogisticRegression(random_state=42)),\n",
       "                             ('rf', RandomForestClassifier(random_state=42)),\n",
       "                             ('svc', SVC(random_state=42))])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.ensemble import VotingClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "log_clf = LogisticRegression(random_state=42)\n",
    "rnd_clf = RandomForestClassifier(random_state=42)\n",
    "svm_clf = SVC(random_state=42)\n",
    "\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='hard')\n",
    "voting_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "80a82744",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.896\n",
      "SVC 0.896\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VotingClassifier 0.912\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "65c732b4",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "VotingClassifier(estimators=[('lr', LogisticRegression(random_state=42)),\n",
       "                             ('rf', RandomForestClassifier(random_state=42)),\n",
       "                             ('svc', SVC(probability=True, random_state=42))],\n",
       "                 voting='soft')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_clf = LogisticRegression(random_state=42)\n",
    "rnd_clf = RandomForestClassifier(random_state=42)\n",
    "svm_clf = SVC(probability=True, random_state=42)\n",
    "\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='soft')\n",
    "voting_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "956f7ec5",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomForestClassifier 0.896\n",
      "SVC 0.896\n",
      "VotingClassifier 0.92\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee527167",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Bagging\n",
    "\n",
    "The **plain** decision trees suffer from high\n",
    "variance. This means that if we split the training data into two parts\n",
    "at random, and fit a decision tree to both halves, the results that we\n",
    "get could be quite different. In contrast, a procedure with low\n",
    "variance will yield similar results if applied repeatedly to distinct\n",
    "data sets; linear regression tends to have low variance, if the ratio\n",
    "of $n$ to $p$ is moderately large. \n",
    "\n",
    "**Bootstrap aggregation**, or just **bagging**, is a\n",
    "general-purpose procedure for reducing the variance of a statistical\n",
    "learning method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "354baed9",
   "metadata": {
    "editable": true
   },
   "source": [
    "## More bagging\n",
    "\n",
    "Bagging typically results in improved accuracy\n",
    "over prediction using a single tree. Unfortunately, however, it can be\n",
    "difficult to interpret the resulting model. Recall that one of the\n",
    "advantages of decision trees is the attractive and easily interpreted\n",
    "diagram that results.\n",
    "\n",
    "However, when we bag a large number of trees, it is no longer\n",
    "possible to represent the resulting statistical learning procedure\n",
    "using a single tree, and it is no longer clear which variables are\n",
    "most important to the procedure. Thus, bagging improves prediction\n",
    "accuracy at the expense of interpretability.  Although the collection\n",
    "of bagged trees is much more difficult to interpret than a single\n",
    "tree, one can obtain an overall summary of the importance of each\n",
    "predictor using the MSE (for bagging regression trees) or the Gini\n",
    "index (for bagging classification trees). In the case of bagging\n",
    "regression trees, we can record the total amount that the MSE is\n",
    "decreased due to splits over a given predictor, averaged over all $B$ possible\n",
    "trees. A large value indicates an important predictor. Similarly, in\n",
    "the context of bagging classification trees, we can add up the total\n",
    "amount that the Gini index  is decreased by splits over a given\n",
    "predictor, averaged over all $B$ trees."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1a2451",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Making your own Bootstrap: Changing the Level of the Decision Tree\n",
    "\n",
    "Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with\n",
    "a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points $n$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "129bb9fb",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial degree: 1\n",
      "Error: 0.06380941468319971\n",
      "Bias^2: 0.05160313473529168\n",
      "Var: 0.01220627994790804\n",
      "0.06380941468319971 >= 0.05160313473529168 + 0.01220627994790804 = 0.06380941468319971\n",
      "Polynomial degree: 2\n",
      "Error: 0.043464037468677004\n",
      "Bias^2: 0.02659851591375224\n",
      "Var: 0.01686552155492476\n",
      "0.043464037468677004 >= 0.02659851591375224 + 0.01686552155492476 = 0.043464037468677\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial degree: 3\n",
      "Error: 0.020716391693769383\n",
      "Bias^2: 0.01159033914386312\n",
      "Var: 0.00912605254990626\n",
      "0.020716391693769383 >= 0.01159033914386312 + 0.00912605254990626 = 0.02071639169376938\n",
      "Polynomial degree: 4\n",
      "Error: 0.02063627410934057\n",
      "Bias^2: 0.0117496656370668\n",
      "Var: 0.008886608472273775\n",
      "0.02063627410934057 >= 0.0117496656370668 + 0.008886608472273775 = 0.020636274109340574\n",
      "Polynomial degree: 5\n",
      "Error: 0.02087627881701288\n",
      "Bias^2: 0.01349183949256158\n",
      "Var: 0.007384439324451296\n",
      "0.02087627881701288 >= 0.01349183949256158 + 0.007384439324451296 = 0.020876278817012876\n",
      "Polynomial degree: 6\n",
      "Error: 0.02069601123831537\n",
      "Bias^2: 0.013918526350129823\n",
      "Var: 0.0067774848881855445\n",
      "0.02069601123831537 >= 0.013918526350129823 + 0.0067774848881855445 = 0.020696011238315368\n",
      "Polynomial degree: 7\n",
      "Error: 0.022964339924731444\n",
      "Bias^2: 0.01550381208433455\n",
      "Var: 0.007460527840396904\n",
      "0.022964339924731444 >= 0.01550381208433455 + 0.007460527840396904 = 0.022964339924731455\n",
      "Simple tree: 0.5148389267750961\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_94_2.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.utils import resample\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "n = 100\n",
    "n_boostraps = 100\n",
    "maxdepth = 8\n",
    "\n",
    "# Make data set.\n",
    "x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
    "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
    "error = np.zeros(maxdepth)\n",
    "bias = np.zeros(maxdepth)\n",
    "variance = np.zeros(maxdepth)\n",
    "polydegree = np.zeros(maxdepth)\n",
    "X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "# we produce a simple tree first as benchmark\n",
    "simpletree = DecisionTreeRegressor(max_depth=3) \n",
    "simpletree.fit(X_train_scaled, y_train)\n",
    "simpleprediction = simpletree.predict(X_test_scaled)\n",
    "for degree in range(1,maxdepth):\n",
    "    model = DecisionTreeRegressor(max_depth=degree) \n",
    "    y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
    "    for i in range(n_boostraps):\n",
    "        x_, y_ = resample(X_train_scaled, y_train)\n",
    "        model.fit(x_, y_)\n",
    "        y_pred[:, i] = model.predict(X_test_scaled)#.ravel()\n",
    "\n",
    "    polydegree[degree] = degree\n",
    "    error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
    "    bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
    "    variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
    "    print('Polynomial degree:', degree)\n",
    "    print('Error:', error[degree])\n",
    "    print('Bias^2:', bias[degree])\n",
    "    print('Var:', variance[degree])\n",
    "    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
    " \n",
    "mse_simpletree= np.mean( np.mean((y_test - simpleprediction)**2))\n",
    "print(\"Simple tree:\",mse_simpletree)\n",
    "plt.xlim(1,maxdepth)\n",
    "plt.plot(polydegree, error, label='MSE')\n",
    "plt.plot(polydegree, bias, label='bias')\n",
    "plt.plot(polydegree, variance, label='Variance')\n",
    "plt.legend()\n",
    "save_fig(\"baggingboot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "170b00ab",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Random forests\n",
    "\n",
    "Random forests provide an improvement over bagged trees by way of a\n",
    "small tweak that decorrelates the trees. \n",
    "\n",
    "As in bagging, we build a\n",
    "number of decision trees on bootstrapped training samples. But when\n",
    "building these decision trees, each time a split in a tree is\n",
    "considered, a random sample of $m$ predictors is chosen as split\n",
    "candidates from the full set of $p$ predictors. The split is allowed to\n",
    "use only one of those $m$ predictors. \n",
    "\n",
    "A fresh sample of $m$ predictors is\n",
    "taken at each split, and typically we choose"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58a4aa65",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "m\\approx \\sqrt{p}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5ed07c1",
   "metadata": {
    "editable": true
   },
   "source": [
    "In building a random forest, at\n",
    "each split in the tree, the algorithm is not even allowed to consider\n",
    "a majority of the available predictors. \n",
    "\n",
    "The reason for this is rather clever. Suppose that there is one very\n",
    "strong predictor in the data set, along with a number of other\n",
    "moderately strong predictors. Then in the collection of bagged\n",
    "variable importance random forest trees, most or all of the trees will\n",
    "use this strong predictor in the top split. Consequently, all of the\n",
    "bagged trees will look quite similar to each other. Hence the\n",
    "predictions from the bagged trees will be highly correlated.\n",
    "Unfortunately, averaging many highly correlated quantities does not\n",
    "lead to as large of a reduction in variance as averaging many\n",
    "uncorrelated quantities. In particular, this means that bagging will\n",
    "not lead to a substantial reduction in variance over a single tree in\n",
    "this setting."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5369edb",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Random Forest Algorithm\n",
    "The algorithm described here can be applied to both classification and regression problems.\n",
    "\n",
    "We will grow of forest of say $B$ trees.\n",
    "1. For $b=1:B$\n",
    "\n",
    "  * Draw a bootstrap sample from the training data organized in our $\\boldsymbol{X}$ matrix.\n",
    "\n",
    "  * We grow then a random forest tree $T_b$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached\n",
    "\n",
    "1. we select $m \\le p$ variables at random from the $p$ predictors/features\n",
    "\n",
    "2. pick the best split point among the $m$ features using for example the CART algorithm and create a new node\n",
    "\n",
    "3. split the node into daughter nodes\n",
    "\n",
    "4. Output then the ensemble of trees $\\{T_b\\}_1^{B}$ and make predictions for either a regression type of problem or a classification type of problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4355c5ad",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Random Forests Compared with other Methods on the Cancer Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0fbcd18f",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(426, 30)\n",
      "(143, 30)\n",
      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
      "Test set accuracy SVM with scaled data: 0.96\n",
      "Test set accuracy with Decision Trees and scaled data: 0.87\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.93333333 0.73333333 0.93333333 1.         1.         0.92857143\n",
      " 1.         0.92857143 0.92857143 0.92857143]\n",
      "Test set accuracy with Random Forests and scaled data: 0.98\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_100_2.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_100_3.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_100_4.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "\n",
    "# Load the data\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "#define methods\n",
    "# Logistic Regression\n",
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "# Support vector machine\n",
    "svm = SVC(gamma='auto', C=100)\n",
    "# Decision Trees\n",
    "deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
    "#Scale the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "# Logistic Regression\n",
    "logreg.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Support Vector Machine\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))\n",
    "\n",
    "\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.model_selection import cross_validate\n",
    "# Data set not specificied\n",
    "#Instantiate the model with 500 trees and entropy as splitting criteria\n",
    "Random_Forest_model = RandomForestClassifier(n_estimators=500,criterion=\"entropy\")\n",
    "Random_Forest_model.fit(X_train_scaled, y_train)\n",
    "#Cross validation\n",
    "accuracy = cross_validate(Random_Forest_model,X_test_scaled,y_test,cv=10)['test_score']\n",
    "print(accuracy)\n",
    "print(\"Test set accuracy with Random Forests and scaled data: {:.2f}\".format(Random_Forest_model.score(X_test_scaled,y_test)))\n",
    "\n",
    "\n",
    "import scikitplot as skplt\n",
    "y_pred = Random_Forest_model.predict(X_test_scaled)\n",
    "skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
    "plt.show()\n",
    "y_probas = Random_Forest_model.predict_proba(X_test_scaled)\n",
    "skplt.metrics.plot_roc(y_test, y_probas)\n",
    "plt.show()\n",
    "skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4072de62",
   "metadata": {
    "editable": true
   },
   "source": [
    "Recall that the cumulative gains curve shows the percentage of the\n",
    "overall number of cases in a given category *gained* by targeting a\n",
    "percentage of the total number of cases.\n",
    "\n",
    "Similarly, the receiver operating characteristic curve, or ROC curve,\n",
    "displays the diagnostic ability of a binary classifier system as its\n",
    "discrimination threshold is varied. It plots the true positive rate against the false positive rate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "481673fb",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Compare  Bagging on Trees with Random Forests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d5fe5939",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "bag_clf = BaggingClassifier(\n",
    "    DecisionTreeClassifier(splitter=\"random\", max_leaf_nodes=16, random_state=42),\n",
    "    n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7ee6160d",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9790209790209791"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bag_clf.fit(X_train, y_train)\n",
    "y_pred = bag_clf.predict(X_test)\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)\n",
    "rnd_clf.fit(X_train, y_train)\n",
    "y_pred_rf = rnd_clf.predict(X_test)\n",
    "np.sum(y_pred == y_pred_rf) / len(y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a6e484c",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Boosting, a Bird's Eye View\n",
    "\n",
    "The basic idea is to combine weak classifiers in order to create a good\n",
    "classifier. With a weak classifier we often intend a classifier which\n",
    "produces results which are only slightly better than we would get by\n",
    "random guesses.\n",
    "\n",
    "This is done by applying in an iterative way a weak (or a standard\n",
    "classifier like decision trees) to modify the data. In each iteration\n",
    "we emphasize those observations which are misclassified by weighting\n",
    "them with a factor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed91ea28",
   "metadata": {
    "editable": true
   },
   "source": [
    "## What is boosting? Additive Modelling/Iterative Fitting\n",
    "\n",
    "Boosting is a way of fitting an additive expansion in a set of\n",
    "elementary basis functions like for example some simple polynomials.\n",
    "Assume for example that we have a function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ab6f212",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "288a57f1",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $\\beta_m$ are the expansion parameters to be determined in a\n",
    "minimization process and $b(x;\\gamma_m)$ are some simple functions of\n",
    "the multivariable parameter $x$ which is characterized by the\n",
    "parameters $\\gamma_m$.\n",
    "\n",
    "As an example, consider the Sigmoid function we used in logistic\n",
    "regression. In that case, we can translate the function\n",
    "$b(x;\\gamma_m)$ into the Sigmoid function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0ea7a14",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sigma(t) = \\frac{1}{1+\\exp{(-t)}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faa1b446",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $t=\\gamma_0+\\gamma_1 x$ and the parameters $\\gamma_0$ and\n",
    "$\\gamma_1$ were determined by the Logistic Regression fitting\n",
    "algorithm.\n",
    "\n",
    "As another example, consider the cost function we defined for linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a20c6de5",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17800601",
   "metadata": {
    "editable": true
   },
   "source": [
    "In this case the function $f(x)$ was replaced by the design matrix\n",
    "$\\boldsymbol{X}$ and the unknown linear regression parameters $\\boldsymbol{\\beta}$,\n",
    "that is $\\boldsymbol{f}=\\boldsymbol{X}\\boldsymbol{\\beta}$. In linear regression we can \n",
    "simply invert a matrix and obtain the parameters $\\beta$ by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b59e224",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{\\beta}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5917a9a",
   "metadata": {
    "editable": true
   },
   "source": [
    "In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters $\\beta_m$ and $\\gamma_m$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d2101f2",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Iterative Fitting, Regression and Squared-error Cost Function\n",
    "\n",
    "The way we proceed is as follows (here we specialize to the squared-error cost function)\n",
    "\n",
    "1. Establish a cost function, here $C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ with $f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m)$.\n",
    "\n",
    "2. Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.\n",
    "\n",
    "3. For $m=1:M$\n",
    "\n",
    "a. minimize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2$ wrt $\\gamma$ and $\\beta$\n",
    "\n",
    "b. This gives the optimal values $\\beta_m$ and $\\gamma_m$\n",
    "\n",
    "c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)$\n",
    "\n",
    "We could use any of the algorithms we have discussed till now. If we\n",
    "use trees, $\\gamma$ parameterizes the split variables and split points\n",
    "at the internal nodes, and the predictions at the terminal nodes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65f77895",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Squared-Error Example and Iterative Fitting\n",
    "\n",
    "To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.\n",
    "\n",
    "For simplicity we assume also that our functions $b(x;\\gamma)=1+\\gamma x$. \n",
    "\n",
    "This means that for every iteration $m$, we need to optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28b76851",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "(\\beta_m,\\gamma_m) = \\mathrm{argmin}_{\\beta,\\lambda}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2=\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta(1+\\gamma x_i))^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "985ccfb2",
   "metadata": {
    "editable": true
   },
   "source": [
    "We start our iteration by simply setting $f_0(x)=0$. \n",
    "Taking the derivatives  with respect to $\\beta$ and $\\gamma$ we obtain"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05d75812",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\frac{\\partial {\\cal C}}{\\partial \\beta} = -2\\sum_{i}(1+\\gamma x_i)(y_i-\\beta(1+\\gamma x_i))=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cfc5c74",
   "metadata": {
    "editable": true
   },
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3833eb7b",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\frac{\\partial {\\cal C}}{\\partial \\gamma} =-2\\sum_{i}\\beta x_i(y_i-\\beta(1+\\gamma x_i))=0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fca374c",
   "metadata": {
    "editable": true
   },
   "source": [
    "We can then rewrite these equations as (defining $\\boldsymbol{w}=\\boldsymbol{e}+\\gamma \\boldsymbol{x})$ with $\\boldsymbol{e}$ being the unit vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aeb623d7",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\gamma \\boldsymbol{w}^T(\\boldsymbol{y}-\\beta\\gamma \\boldsymbol{w})=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8e542a2",
   "metadata": {
    "editable": true
   },
   "source": [
    "which gives us $\\beta = \\boldsymbol{w}^T\\boldsymbol{y}/(\\boldsymbol{w}^T\\boldsymbol{w})$. Similarly we have"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d92e3136",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\beta\\gamma \\boldsymbol{x}^T(\\boldsymbol{y}-\\beta(1+\\gamma \\boldsymbol{x}))=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bca4d27a",
   "metadata": {
    "editable": true
   },
   "source": [
    "which leads to $\\gamma =(\\boldsymbol{x}^T\\boldsymbol{y}-\\beta\\boldsymbol{x}^T\\boldsymbol{e})/(\\beta\\boldsymbol{x}^T\\boldsymbol{x})$.  Inserting\n",
    "for $\\beta$ gives us an equation for $\\gamma$. This is a non-linear equation in the unknown $\\gamma$ and has to be solved numerically. \n",
    "\n",
    "The solution to these two equations gives us in turn $\\beta_1$ and $\\gamma_1$ leading to the new expression for $f_1(x)$ as\n",
    "$f_1(x) = \\beta_1(1+\\gamma_1x)$. Doing this $M$ times results in our final estimate for the function $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2fa1316",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Iterative Fitting, Classification and AdaBoost\n",
    "\n",
    "Let us consider a binary classification problem with two outcomes $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
    "observations. We define a classification function $G(x)$ which produces a prediction taking one or the other of the two values \n",
    "$\\{-1,1\\}$.\n",
    "\n",
    "The error rate of the training sample is then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5401b686",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mathrm{\\overline{err}}=\\frac{1}{n} \\sum_{i=0}^{n-1} I(y_i\\ne G(x_i)).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "082464c4",
   "metadata": {
    "editable": true
   },
   "source": [
    "The iterative procedure starts with defining a weak classifier whose\n",
    "error rate is barely better than random guessing.  The iterative\n",
    "procedure in boosting is to sequentially apply a  weak\n",
    "classification algorithm to repeatedly modified versions of the data\n",
    "producing a sequence of weak classifiers $G_m(x)$.\n",
    "\n",
    "Here we will express our  function $f(x)$ in terms of $G(x)$. That is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f2a4a17",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4aad349a",
   "metadata": {
    "editable": true
   },
   "source": [
    "will be a function of"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2050bb1",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "G_M(x) = \\mathrm{sign} \\sum_{i=1}^M \\alpha_m G_m(x).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "359b0eb3",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Adaptive Boosting, AdaBoost\n",
    "\n",
    "In our iterative procedure we define thus"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eab77ff9",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "f_m(x) = f_{m-1}(x)+\\beta_mG_m(x).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7c87ec5",
   "metadata": {
    "editable": true
   },
   "source": [
    "The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the\n",
    "exponential cost/loss function defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cf53a5f",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{(-y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67bbb3ac",
   "metadata": {
    "editable": true
   },
   "source": [
    "We optimize $\\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.\n",
    "This is normally done in two steps. Let us however first rewrite the cost function as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9a2448e",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{(-y_i\\beta G(x_i))},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "392f16f2",
   "metadata": {
    "editable": true
   },
   "source": [
    "where we have defined $w_i^m= \\exp{(-y_if_{m-1}(x_i))}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a645e83c",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Building up AdaBoost\n",
    "\n",
    "First, for any $\\beta > 0$, we optimize $G$ by setting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89e1d11e",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "G_m(x) = \\mathrm{sign} \\sum_{i=0}^{n-1} w_i^m I(y_i \\ne G_(x_i)),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f884f217",
   "metadata": {
    "editable": true
   },
   "source": [
    "which is the classifier that minimizes the weighted error rate in predicting $y$.\n",
    "\n",
    "We can do this by rewriting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "664acf19",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\exp{-(\\beta)}\\sum_{y_i=G(x_i)}w_i^m+\\exp{(\\beta)}\\sum_{y_i\\ne G(x_i)}w_i^m,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d83ebe5e",
   "metadata": {
    "editable": true
   },
   "source": [
    "which can be rewritten as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96134017",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "(\\exp{(\\beta)}-\\exp{-(\\beta)})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{(-\\beta)}\\sum_{i=0}^{n-1}w_i^m=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97fc79c8",
   "metadata": {
    "editable": true
   },
   "source": [
    "which leads to"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d1e4f3e",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\beta_m = \\frac{1}{2}\\log{\\frac{1-\\mathrm{\\overline{err}}}{\\mathrm{\\overline{err}}}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d571a24",
   "metadata": {
    "editable": true
   },
   "source": [
    "where we have redefined the error as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f31a3a7",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mathrm{\\overline{err}}_m=\\frac{1}{n}\\frac{\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i)}{\\sum_{i=0}^{n-1}w_i^m},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0e3db77",
   "metadata": {
    "editable": true
   },
   "source": [
    "which leads to an update of"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1ce185",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "f_m(x) = f_{m-1}(x) +\\beta_m G_m(x).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7360d72",
   "metadata": {
    "editable": true
   },
   "source": [
    "This leads to the new weights"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf486320",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "w_i^{m+1} = w_i^m \\exp{(-y_i\\beta_m G_m(x_i))}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ebdf8ce",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Adaptive boosting: AdaBoost, Basic Algorithm\n",
    "\n",
    "The algorithm here is rather straightforward. Assume that our weak\n",
    "classifier is a decision tree and we consider a binary set of outputs\n",
    "with $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
    "observations. Our design matrix is given in terms of the\n",
    "feature/predictor vectors\n",
    "$\\boldsymbol{X}=[\\boldsymbol{x}_0\\boldsymbol{x}_1\\dots\\boldsymbol{x}_{p-1}]$. Finally, we define also a\n",
    "classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\\boldsymbol{y}$. \n",
    "\n",
    "We have already defined the misclassification error $\\mathrm{err}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "853a1218",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i)),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d287b19d",
   "metadata": {
    "editable": true
   },
   "source": [
    "where the function $I()$ is one if we misclassify and zero if we classify correctly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "637ef064",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Basic Steps of AdaBoost\n",
    "\n",
    "With the above definitions we are now ready to set up the algorithm for AdaBoost.\n",
    "The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.\n",
    "1. We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\\dots n-1$. It is easy to see that we must have $\\sum_{i=0}^{n-1}w_i = 1$.\n",
    "\n",
    "2. We rewrite the misclassification error as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1698dc3",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mathrm{\\overline{err}}_m=\\frac{\\sum_{i=0}^{n-1}w_i^m I(y_i\\ne G(x_i))}{\\sum_{i=0}^{n-1}w_i},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6d08c01",
   "metadata": {
    "editable": true
   },
   "source": [
    "1. Then we start looping over all attempts at classifying, namely we start an iterative process for $m=1:M$, where $M$ is the final number of classifications. Our given classifier could for example be a plain decision tree.\n",
    "\n",
    "a. Fit then a given classifier to the training set using the weights $w_i$.\n",
    "\n",
    "b. Compute then $\\mathrm{err}$ and figure out which events are classified properly and which are classified wrongly.\n",
    "\n",
    "c. Define a quantity $\\alpha_{m} = \\log{(1-\\mathrm{\\overline{err}}_m)/\\mathrm{\\overline{err}}_m}$\n",
    "\n",
    "d. Set the new weights to $w_i = w_i\\times \\exp{(\\alpha_m I(y_i\\ne G(x_i)}$.\n",
    "\n",
    "5. Compute the new classifier $G(x)= \\sum_{i=0}^{n-1}\\alpha_m I(y_i\\ne G(x_i)$.\n",
    "\n",
    "For the iterations with $m \\le 2$ the weights are modified\n",
    "individually at each steps. The observations which were misclassified\n",
    "at iteration $m-1$ have a weight which is larger than those which were\n",
    "classified properly. As this proceeds, the observations which were\n",
    "difficult to classifiy correctly are given a larger influence. Each\n",
    "new classification step $m$ is then forced to concentrate on those\n",
    "observations that are missed in the previous iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c58db919",
   "metadata": {
    "editable": true
   },
   "source": [
    "## AdaBoost Examples\n",
    "\n",
    "Using **Scikit-Learn** it is easy to apply the adaptive boosting algorithm, as done here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "104e1c7c",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_161_0.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_161_1.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week46_161_2.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "ada_clf = AdaBoostClassifier(\n",
    "    DecisionTreeClassifier(max_depth=1), n_estimators=200,\n",
    "    algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n",
    "ada_clf.fit(X_train, y_train)\n",
    "\n",
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "ada_clf = AdaBoostClassifier(\n",
    "    DecisionTreeClassifier(max_depth=1), n_estimators=200,\n",
    "    algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n",
    "ada_clf.fit(X_train_scaled, y_train)\n",
    "y_pred = ada_clf.predict(X_test_scaled)\n",
    "skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
    "plt.show()\n",
    "y_probas = ada_clf.predict_proba(X_test_scaled)\n",
    "skplt.metrics.plot_roc(y_test, y_probas)\n",
    "plt.show()\n",
    "skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}